Learn Russian: У подделки этикетка такая же, как у оригинала. - The counterfeit's label is exactly the same as the original's.

такая agrees with the feminine noun этикетка (label). The phrase такой же ... как acts like an adjective, so it must match the gender, case, and number of the noun it describes. If we were comparing actions (adverbs) rather than nouns, we would use the unchangeable так же.

Why does the sentence use у подделки instead of just putting the word for 'counterfeit' in the genitive case?

While you could say этикетка подделки (the label of the counterfeit), Russian frequently uses the у + genitive construction to show possession (literally, 'at the counterfeit'). By repeating у later in the sentence (у оригинала), it creates a very natural, balanced comparison between what the two items 'have'.

Are подделки and оригинала both in the genitive case here?

Yes. Both nouns follow the preposition у, which always requires the genitive case. The feminine noun подделка changes to подделки, and the masculine noun оригинал gets an -а added to become оригинала.

Is the comma before как optional?

No, it is strictly required. In Russian punctuation, you must always put a comma before как when it sets up a comparison clause, such as in the такой же, как (the same as) structure.